Finite Group Databasebeta

← #33022628

Subgroups — #33022628

Order 18688.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988522C212yesmaximal
2C2×#17988485C211yesmaximal, characteristic, complemented
3C2×#17988456C211yesmaximal, characteristic, complemented
4C2×#17988444C211yesmaximal, characteristic
5C2×#17988444C211yesmaximal, characteristic
6C2×C4×#11924005C211yesmaximal, characteristic
7#22608197C212yesmaximal, complemented
8#22608194C212yesmaximal, complemented
9#22608175C212yesmaximal
10#22608160C211yesmaximal, characteristic, complemented
11C2×#389×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2211yescharacteristic
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×#11924007C2212yes—
18C22×#11924005C2212yes—
19C22×#11924005C2212yes—
20C22×#11924005C2211yescharacteristic
21C22×#11924005C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23#17988522—28no—
24#17988485—24no—
25#17988456—24no—
26#17988444—24no—
27#17988444—24no—
28C4×#11924005—24no—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C4⋊C4×C73C2212yes—
38C22×C4⋊C4×C73C2211yescharacteristic
39C22×C42×C73C2211yescharacteristic
40#389×C73—24no—
41C2×#95×C73C2212yes—
42C24×D73C2311yescharacteristic
43C23×Dic73C2312yes—
44C23×Dic73C2312yes—
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C23×Dic73C2311yescharacteristic
48C22×C4×D73—22no—
49C22×C4×D73—22no—
50C22×C4×D73—22no—
51C22×C4×D73—22no—
52C22×C4×D73—22no—
53C22×C4×D73—22no—
54C22×C4×D73Q814yes—
55C2×C4⋊Dic73—22no—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73—22no—
58C2×C4⋊Dic73—22no—
59C2×C4⋊Dic73—22no—
60C2×C4⋊Dic73D414yes—
61C2×#11924007—24no—
62C2×#11924007—24no—
63C2×#11924007—24no—
64C2×#11924007—24no—
65C2×#11924007—24no—
66C2×#11924007—24no—
67C2×#11924007—42no—
68C2×#11924007—42no—
69C2×#11924007—42no—
70C2×#11924005—22no—
71C2×#11924005—22no—
72C2×#11924005—22no—
73C2×#11924005—22no—
74C2×#11924005—24no—
75C2×#11924005—24no—
76C2×#11924005—24no—
77C2×#11924005—24no—
78C2×#11924005—42no—
79C2×#11924005—42no—
80C2×#11924005D414yes—
81C2×#11924005Q814yes—
82C2×C4×Dic73—22no—
83C2×C4×Dic73—22no—
84C2×C4×Dic73D414yes—
85#14556498—22no—
86#14556498—22no—
87#14556498—24no—
88#14556498—24no—
89#14556498—24no—
90#14556498—24no—
91#14556498—24no—
92C23×C4×C73C2312yes—
93C23×C4×C73C2312yes—
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73—22no—
99C2×C4⋊C4×C73—24no—
100C2×C4⋊C4×C73—22no—
101C2×C4⋊C4×C73—22no—
102C2×C4⋊C4×C73—22no—
103C2×C4⋊C4×C73—24no—
104C2×C4⋊C4×C73—42no—
105C2×C4⋊C4×C73D414yes—
106C2×C42×C73—22no—
107C2×C42×C73—22no—
108C2×C42×C73—22no—
109#95×C73—24no—
110C23×D73—21no—
111C23×D73—21no—
112C23×D73—21no—
113C23×D73—21no—
114C23×D73—21no—
115C23×D73—21no—
116C23×D73—21no—
117C23×D73—21no—
118C23×D73—21no—
119C23×D73—21no—
120C23×D73—21no—
121C23×D73—21no—
122C23×D73C2×D412yes—
123C23×D73C2×Q812yes—
124C23×D73C2×Q812yes—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73—22no—
147C22×Dic73—22no—
148C22×Dic73—22no—
149C22×Dic73—22no—
150C22×Dic73—22no—
151C22×Dic73—22no—
152C22×Dic73C2×D414yes—
153C22×Dic73C2×D412yes—
154C22×Dic73C2×D412yes—
155C22×Dic73C2×D412yes—
156C22×Dic73C2×Q812yes—
157C22×Dic73C2×Q812yes—
158C22×Dic73#4112yes—
159C22×Dic73#4112yes—
160C2×C4×D73—28no—
161C2×C4×D73—28no—
162C2×C4×D73—28no—
163C2×C4×D73—44no—
164C2×C4×D73—44no—
165C2×C4×D73—44no—
166C2×C4×D73—44no—
167C4⋊Dic73—28no—
168C4⋊Dic73—44no—
169#11924007—48no—
170#11924007—48no—
171#11924007—48no—
172#11924005—28no—
173#11924005—28no—
174#11924005—48no—
175#11924005—48no—
176C4×Dic73—28no—
177C24×C73C2411yescharacteristic
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—22no—
187C22×C4×C73—22no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—22no—
192C22×C4×C73—21no—
193C22×C4×C73—22no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—22no—
197C22×C4×C73—22no—
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—22no—
202C22×C4×C73—22no—
203C22×C4×C73C2×D412yes—
204C22×C4×C73C2×D412yes—
205C22×C4×C73C2×D412yes—
206C22×C4×C73C2×D414yes—
207C22×C4×C73C2×D412yes—
208C22×C4×C73C2×Q812yes—
209C22×C4×C73C2×Q812yes—
210C22×C4×C73#4112yes—
211C22×C4×C73#4112yes—
212C22×C4×C73#4112yes—
213C4⋊C4×C73—28no—
214C4⋊C4×C73—48no—
215C4⋊C4×C73—44no—
216C42×C73—44no—
217C23×C73C22×D411yescharacteristic
218C23×C73C22×D411yescharacteristic
219C23×C73C22×D411yescharacteristic
220C23×C73C22×D411yescharacteristic
221C23×C73C22×Q811yescharacteristic
222C23×C73C22×Q811yescharacteristic
223C23×C73C2×#4111yescharacteristic
224C23×C73C2×#4111yescharacteristic
225C23×C73C2×#4111yescharacteristic
226C23×C73C2×#4111yescharacteristic
227C23×C73C2×#4111yescharacteristic
228C23×C73H(5,𝔽2)11yescharacteristic
229C23×C73H(5,𝔽2)11yescharacteristic
230C23×C732−1+411yescharacteristic
231C23×C732−1+411yescharacteristic
232C22×D73—22no—
233C22×D73—22no—
234C22×D73—22no—
235C22×D73—22no—
236C22×D73—22no—
237C22×D73—22no—
238C22×D73—22no—
239C22×D73—22no—
240C22×D73—22no—
241C22×D73—22no—
242C22×D73—22no—
243C22×D73—22no—
244C22×D73—22no—
245C22×D73—22no—
246C22×D73—22no—
247C22×D73—22no—
248C22×D73—22no—
249C22×D73—22no—
250C22×D73—41no—
251C22×D73—41no—
252C22×D73—41no—
253C22×D73—41no—
254C22×D73—41no—
255C22×D73—41no—
256C22×D73—41no—
257C22×D73—41no—
258C22×D73—41no—
259C22×D73—41no—
260C22×D73—41no—
261C22×D73—41no—
262C22×D73—41no—
263C22×D73—41no—
264C22×D73—41no—
265C22×D73—41no—
266C22×D73C4⋊Q814yes—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—24no—
270C2×C4×C73—22no—
271C2×C4×C73—24no—
272C2×C4×C73—22no—
273C2×C4×C73—24no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—42no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—42no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—42no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—42no—
288C2×C4×C73—42no—
289C2×C4×C73—42no—
290C2×C4×C73—42no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73C22⋊Q814yes—
296C2×C4×C73C22⋊Q814yes—
297C2×C4×C73C22⋊Q814yes—
298C2×C4×C73#12314yes—
299C2×C4×C73#12314yes—
300C2×C4×C73#12314yes—
301C2×C4×C73#12714yes—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—24no—
318C2×Dic73—24no—
319C2×Dic73—24no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73—42no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334C2×Dic73—42no—
335C2×Dic73#12114yes—
336C2×Dic73C22⋊Q814yes—
337C4×D73—416no—
338C22×C73C2×#12111yescharacteristic
339C22×C73C2×C22⋊Q811yescharacteristic
340C22×C73C2×C22⋊Q811yescharacteristic
341C22×C73C2×C22⋊Q811yescharacteristic
342C22×C73C2×C22⋊Q811yescharacteristic
343C22×C73C2×#12311yescharacteristic
344C22×C73C2×#12311yescharacteristic
345C22×C73C2×#12311yescharacteristic
346C22×C73C2×#12711yescharacteristic
347C22×C73C2×C4⋊Q811yescharacteristic
348C22×C73#53211yescharacteristic
349C22×C73#53311yescharacteristic
350C22×C73#53311yescharacteristic
351C22×C73#53511yescharacteristic
352C22×C73#53611yescharacteristic
353C22×C73#54211yescharacteristic
354C22×C73#54211yescharacteristic
355C22×C73#54411yescharacteristic
356C22×C73#54411yescharacteristic
357C22×C73D4211yescharacteristic
358C22×C73D4211yescharacteristic
359C22×C73#54711yescharacteristic
360C22×C73#54711yescharacteristic
361C22×C73#54711yescharacteristic
362C22×C73#54711yescharacteristic
363C22×C73D4×Q811yescharacteristic
364C22×C73D4×Q811yescharacteristic
365C22×C73#55011yescharacteristic
366C22×C73#55011yescharacteristic
367C22×C73#55211yescharacteristic
368C22×C73#55211yescharacteristic
369C22×C73#55311yescharacteristic
370C22×C73#55311yescharacteristic
371C22×C73#55411yescharacteristic
372C22×C73#55411yescharacteristic
373C2×D73—24no—
374C2×D73—24no—
375C2×D73—24no—
376C2×D73—42no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C2×D73—42no—
383C2×D73—42no—
384C2×D73—42no—
385C2×D73—42no—
386C2×D73—42no—
387C2×D73—42no—
388C4×C73—44no—
389C4×C73—42no—
390C4×C73—42no—
391C4×C73—82no—
392C4×C73#39918yescomplemented
393Dic73—24no—
394Dic73—24no—
395Dic73—42no—
396Dic73—44no—
397Dic73—82no—
398#15135—731nomaximal, Sylow
399C2×C73C2×#39911yescharacteristic
400C2×C73#242211yescharacteristic
401C2×C73#242211yescharacteristic
402C2×C73#242311yescharacteristic
403C2×C73#242311yescharacteristic
404C2×C73#244011yescharacteristic
405C2×C73#244011yescharacteristic
406C2×C73#244111yescharacteristic
407C2×C73#244111yescharacteristic
408C2×C73#248611yescharacteristic
409C2×C73#248711yescharacteristic
410C2×C73#254111yescharacteristic
411C2×C73#254211yescharacteristic
412C2×C73#262811yescharacteristic
413C2×C73#285711yescharacteristic
414D73—44no—
415C2×#399—732no—
416C2×#389—731no—
417C2×#389D7311yescharacteristic, complemented
418C2×#384—731no—
419C2×#380—731no—
420C2×#380—731no—
421C2×C4×C22⋊C4—731no—
422#1445—732no—
423#1444—732no—
424#1439—732no—
425C4⋊#95—731no—
426C73#1513511yescharacteristic, complemented, Sylow
427C24×C4—731no—
428C22×C4⋊C4—732no—
429C22×C4⋊C4—732no—
430C22×C4⋊C4—731no—
431C22×C4⋊C4—732no—
432C22×C4⋊C4—731no—
433C22×C4⋊C4C2×D7311yescharacteristic
434C22×C4⋊C4C2×D7312yes—
435C22×C4⋊C4C2×D7311yescharacteristic
436C22×C22⋊C4—732no—
437C22×C22⋊C4—732no—
438C22×C22⋊C4—731no—
439C22×C22⋊C4—731no—
440C22×C42—731no—
441C22×C42C2×D7311yescharacteristic
442#399—1468no—
443#389—24no—
444#389—1464no—
445#384—1464no—
446#380—1464no—
447#380—1464no—
448C4×C22⋊C4—1464no—
449C2×#95—732no—
450C2×#95—732no—
451C2×#95—732no—
452C2×#95—731no—
453C2×#95—732no—
454C2×#95—732no—
455C2×#95—731no—
456C2×#95C2×D7312yes—
457C25—731no—
458C23×C4—731no—
459C23×C4—731no—
460C23×C4—732no—
461C23×C4—731no—
462C23×C4—734no—
463C23×C4—732no—
464C23×C4—1462no—
465C23×C4—1462no—
466C23×C4—1462no—
467C23×C4—1462no—
468C23×C4—1462no—
469C23×C4—1462no—
470C23×C4C22×D7312yes—
471C23×C4C22×D7311yescharacteristic
472C23×C4C22×D7312yes—
473C23×C4C22×D7311yescharacteristic
474C23×C4C22×D7311yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—2922no—
484C2×C4⋊C4—2922no—
485C2×C4⋊C4—2922no—
486C2×C4⋊C4—734no—
487C2×C4⋊C4—1464no—
488C2×C4⋊C4—1464no—
489C2×C4⋊C4—1464no—
490C2×C4⋊C4—1464no—
491C2×C4⋊C4—1464no—
492C2×C4⋊C4—1462no—
493C2×C4⋊C4—1464no—
494C2×C4⋊C4—1462no—
495C2×C4⋊C4—1462no—
496C2×C4⋊C4—1462no—
497C2×C4⋊C4—1462no—
498C2×C4⋊C4C22⋊D7314yes—
499C2×C22⋊C4—2922no—
500C2×C22⋊C4—2922no—
501C2×C22⋊C4—734no—
502C2×C22⋊C4—734no—
503C2×C22⋊C4—1464no—
504C2×C22⋊C4—1464no—
505C2×C22⋊C4—1464no—
506C2×C22⋊C4—1464no—
507C2×C22⋊C4—1462no—
508C2×C22⋊C4—1462no—
509C2×C22⋊C4—1462no—
510C2×C22⋊C4—1462no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—734no—
515C2×C42—1462no—
516C2×C42—1462no—
517#95—24no—
518#95—1464no—
519#95—1462no—
520#95—1462no—
521#95—1464no—
522#95—1464no—
523#95—1464no—
524#95—1464no—
525C24—732no—
526C24—732no—
527C24—732no—
528C24—1461no—
529C24—1461no—
530C24—1461no—
531C24—1461no—
532C24—1461no—
533C24—1461no—
534C24—1461no—
535C24—1461no—
536C24—1461no—
537C24—1461no—
538C24—1461no—
539C24—1461no—
540C24C23×D7311yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—2924no—
567C22×C4—2924no—
568C22×C4—2924no—
569C22×C4—2924no—
570C22×C4—732no—
571C22×C4—732no—
572C22×C4—732no—
573C22×C4—732no—
574C22×C4—732no—
575C22×C4—732no—
576C22×C4—734no—
577C22×C4—732no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1462no—
584C22×C4—1462no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1462no—
588C22×C4—1461no—
589C22×C4—1462no—
590C22×C4—1462no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1462no—
594C22×C4—1461no—
595C22×C4—1462no—
596C22×C4—1462no—
597C22×C4—1468no—
598C22×C4—1468no—
599C22×C4—1468no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4—1461no—
606C22×C4—1461no—
607C22×C4—1461no—
608C22×C4D4×D7312yes—
609C22×C4D4×D7312yes—
610C22×C4D4×D7312yes—
611C22×C4C2×C22⋊D7314yes—
612C22×C4C2×C22⋊D7312yes—
613C22×C4Q8×D7312yes—
614C22×C4Q8×D7312yes—
615C22×C4#1192402812yes—
616C22×C4#1192402812yes—
617C22×C4#1192402912yes—
618C4⋊C4—28no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—2928no—
622C4⋊C4—2928no—
623C4⋊C4—2928no—
624C4⋊C4—2924no—
625C4⋊C4—1468no—
626C22⋊C4—2928no—
627C22⋊C4—2928no—
628C22⋊C4—1468no—
629C22⋊C4—1468no—
630C42—44no—
631C42—1468no—
632C23—2921no—
633C23—2921no—
634C23—2921no—
635C23—2921no—
636C23—2921no—
637C23—2921no—
638C23—2921no—
639C23—2921no—
640C23—2921no—
641C23—2921no—
642C23—2921no—
643C23—2921no—
644C23—2921no—
645C23—2921no—
646C23—2921no—
647C23—2921no—
648C23—734no—
649C23—1462no—
650C23—1462no—
651C23—1462no—
652C23—1462no—
653C23—1462no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23—1462no—
658C23—1462no—
659C23—1462no—
660C23—1462no—
661C23—1462no—
662C23—1462no—
663C23—1462no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23C2×D4×D7311yescharacteristic
668C23C2×D4×D7311yescharacteristic
669C23C2×D4×D7311yescharacteristic
670C23C22×C22⋊D7311yescharacteristic
671C23C2×Q8×D7311yescharacteristic
672C23C2×Q8×D7311yescharacteristic
673C23#41×D7311yescharacteristic
674C23#41×D7311yescharacteristic
675C23C2×#1192402811yescharacteristic
676C23C2×#1192402811yescharacteristic
677C23C2×#1192402911yescharacteristic
678C23#1455663611yescharacteristic
679C23#1455663711yescharacteristic
680C23#1455663811yescharacteristic
681C23#1455663911yescharacteristic
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—2921no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—2922no—
714C2×C4—2922no—
715C2×C4—2921no—
716C2×C4—2921no—
717C2×C4—2921no—
718C2×C4—29216no—
719C2×C4—2922no—
720C2×C4—2922no—
721C2×C4—2922no—
722C2×C4—2922no—
723C2×C4—2922no—
724C2×C4—2922no—
725C2×C4—2922no—
726C2×C4—734no—
727C2×C4—734no—
728C2×C4—1464no—
729C2×C4—1464no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1464no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4#1455656714yes—
747C2×C4#1455656914yes—
748C2×C4#1455656914yes—
749C2×C4#1455657414yes—
750C2×C4#1455657614yes—
751C2×C4#1455657614yes—
752C2×C4#1455658714yes—
753C22—2922no—
754C22—2922no—
755C22—2922no—
756C22—2922no—
757C22—2922no—
758C22—2922no—
759C22—2922no—
760C22—2922no—
761C22—2922no—
762C22—2922no—
763C22—2922no—
764C22—2922no—
765C22—1464no—
766C22—1464no—
767C22—1464no—
768C22#121×D7311yescharacteristic
769C22C22⋊Q8×D7311yescharacteristic
770C22C2×#1455656711yescharacteristic
771C22C2×#1455656911yescharacteristic
772C22C2×#1455656911yescharacteristic
773C22C2×#1455657411yescharacteristic
774C22C2×#1455657611yescharacteristic
775C22C2×#1455657611yescharacteristic
776C22C2×#1455658711yescharacteristic
777C22C4⋊Q8×D7311yescharacteristic
778C22#1798913411yescharacteristic
779C22#1798914111yescharacteristic
780C22#1798914311yescharacteristic
781C22#1798915311yescharacteristic
782C22#1798916011yescharacteristic
783C22#1798920211yescharacteristic
784C22#1798920911yescharacteristic
785C22#1798921411yescharacteristic
786C22#1798921711yescharacteristic
787C22D4×C22⋊D7311yescharacteristic
788C22#1798922111yescharacteristic
789C22#1798923611yescharacteristic
790C22#1798923911yescharacteristic
791C22#1798924011yescharacteristic
792C22#1798924211yescharacteristic
793C22#1798925011yescharacteristic
794C22Q8×C22⋊D7311yescharacteristic
795C22#1798925511yescharacteristic
796C22#1798925611yescharacteristic
797C22#1798927511yescharacteristic
798C22#1798927811yescharacteristic
799C22#1798928711yescharacteristic
800C22#1798929011yescharacteristic
801C22#1798929711yescharacteristic
802C22#1798929811yescharacteristic
803C4—42no—
804C4—42no—
805C4—44no—
806C4—82no—
807C4—2922no—
808C4—2924no—
809C4—5842no—
810C4—1464no—
811C4—1464no—
812C4#1798852218yescomplemented
813C2—2924no—
814C2C2×#1798852211yescharacteristic
815C2#2261343911yescharacteristic
816C2#2261344611yescharacteristic
817C2#2261345011yescharacteristic
818C2#2261345711yescharacteristic
819C2#2261362911yescharacteristic
820C2#2261363511yescharacteristic
821C2#2261364011yescharacteristic
822C2#2261364611yescharacteristic
823C2#2261423711yescharacteristic
824C2#2261424611yescharacteristic
825C2#2261487411yescharacteristic
826C2#2261488111yescharacteristic
827C2#2261575811yescharacteristic
828C2#2261828211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, cosocleC24×C73C24
FittingC2×#389×C73C2
prime radicalC24×D73C23
hypercenterC2×#389D73
hypocenterC73#15135
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#17988485C2semidirect
3. C2×#17988456C2semidirect
7. #22608197C2semidirect
8. #22608194C2semidirect
10. #22608160C2semidirect
11. C2×#389×C73C2semidirect
392. C4×C73#399semidirect
417. C2×#389D73semidirect
426. C73#15135semidirect
812. C4#17988522semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179885222
C2×#179884852
C2×#179884562
C2×#179884442
C2×C4×#119240052
#226081972
#226081942
#226081752
#226081602
C2×#389×C732
#1513573